Urban two-vehicle crashes constitute one of the most significant types of traffic crashes, accounting for a substantial proportion of human casualties and economic losses. Identifying the factors influencing the severity of these crashes can play a crucial role in urban traffic management and safety planning. This study aims to analyze the factors affecting the severity of urban two-vehicle crashes using machine learning models and interpretable methods. The dataset comprised 586 recorded two-vehicle crashes in Shahrud County between 2022 and 2025, extracted from the Traffic Police database. During the preprocessing stage, the data were encoded and balanced, followed by the development of the Random Forest (RF) model as the primary classifier. The performance of the RF model was compared with two baseline models: Logistic Regression (LR) and Decision Tree (DT). Evaluation results indicated that the RF model achieved the best performance in predicting collision severity, with an accuracy of 89%, an AUC of 0.92, and higher Precision, Recall, and F1-score values compared to the other models. To enhance the interpretability of the results, the SHAP method was employed. The findings revealed that the day of the week, vehicle type, time of occurrence, vehicle maneuver, road geometry, lighting conditions, and traffic control are the most significant factors affecting collision severity. Furthermore, the analysis indicated that crashes occurring at night, the absence of traffic control, two-way roads, and the presence of heavy vehicles increase the likelihood of fatal accidents. The results demonstrate that combining machine learning models with interpretable methods can serve as an effective tool for analyzing collision severity and formulating strategies to enhance urban traffic safety.